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Modern Probability and Statistics
V.E. Bening and V.Yu. Korolev
This volume in the Modern Probability and Statistics seriesaims to fill the gap in existing literature on compound Cox processes,i.e. sums of independent identically distributed random variables up toa doubly stochastic Poisson process, which are very important,especially for insurance and financial applications where they providegood asymptotic approximations for basic characteristics such as thedistributions of the surplus of an insurance company under risk andportfolio fluctuations or of increments of stock prices undernon-constant intensity of trade.
It presents the state-of-the-art in the field of compound Cox processesand their applications in insurance and finance. Besides a review ofwell-known classical results on compound and mixed Poisson processes andrisk theory, it contains many new, recently obtained results by theauthors. Among these are: new convergence criteria, convergence rateestimates, asymptotic expansions for quantiles of stochastic processesand many others.
From the applied problems considered in this book, four deserve to bementioned especially: 1) modelling the distribution of increments ofstock prices, closely connected with prediction of the behavior offinancial indexes; 2) the description of asymptotic behavior of theso-called generalized risk processes, which take into account both riskand portfolio fluctuations; 3) statistical estimation of the probabilityof ruin for a generalized risk process; 4) construction of refinedapproximations to the ruin probability, based on its asymptoticexpansions with small safety loading.
This book will be of great value to specialists in applied probabilityand to those who use models and methods of probability theory to solvepractical problems in the fields of insurance and finance.
2002; xx+434 pages
ISBN 90-6764-366-1
Price (all prices are subject to change without notice): EUR 260/US$ 372
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